Definition 18 (Family of Lower Bound Graphs [1]})definition]def:family
Fix an integer \(K\) , a function \(f:\left\lbrace 0,1\right\rbrace ^K\times \left\lbrace 0,1\right\rbrace ^K\rightarrow \left\lbrace \mathrm {true},\mathrm {false}\right\rbrace \)  and a graph predicate \(P\) . A family of graphs
\( \left\lbrace G_{x,y}=(V,E_{x,y}) \mid x,y \in \left\lbrace 0,1\right\rbrace ^K\right\rbrace \) 
